Advanced Number Theory and Mathematical Reasoning Quiz

If a two-digit number's units digit is 2 times its tens digit, and the sum of its digits is 9, what is the number?

• 72
• 18
• 27
• 81

A student answers a quiz where each correct answer earns 10 marks and each incorrect answer loses 5 marks. If the student attempts all questions and scores 160 total marks, how many questions did they answer incorrectly?

• 4
• 2
• 1
• 7

When a number is divided by 5, the remainder is 2. When the same number is divided by 2, the remainder is 0. What must be the last digit of this number?

• 3
• 1
• 7
• 2

If a two-digit number's cost is xy and its selling price is yx (digits interchanged), and the profit margin divided by 9 leaves a remainder, what is that remainder?

• 1
• 0
• 2
• Cannot be determined

When writing all numbers from 1 to 166, how many total digits will be written?

• 512
• 432
• 456
• 478

If a number divided by 5 leaves a remainder of 1, what must be its last digit?

• 6
• 9
• 1
• 4

Two 2-digit numbers have a product of 1392. If the product of their units digits is 42 and tens digits is 8, what are the numbers?

• 17 and 16
• 87 and 16
• 86 and 16
• 87 and 17

A three-digit number subtracted from its digit-reversed version, when divided by 9, leaves what remainder?

• 0
• 1
• 2
• Cannot be determined

A two-digit number's units digit is 2 times its tens digit, and the sum of digits is 9. What is the number?

• 72
• 27
• 18
• 81

Two 2-digit numbers have a product of 2451. If the product of their units digits is 21 and tens digits is 20, what are the numbers?

• 47 and 53
• 43 and 57
• 35 and 74
• 45 and 37